dlagtf(3P) Sun Performance Library dlagtf(3P)NAMEdlagtf - factorize the matrix (T-lambda*I), where T is an n by n tridi‐
agonal matrix and lambda is a scalar, as T-lambda*I = PLU
SYNOPSIS
SUBROUTINE DLAGTF(N, A, LAMBDA, B, C, TOL, D, IN, INFO)
INTEGER N, INFO
INTEGER IN(*)
DOUBLE PRECISION LAMBDA, TOL
DOUBLE PRECISION A(*), B(*), C(*), D(*)
SUBROUTINE DLAGTF_64(N, A, LAMBDA, B, C, TOL, D, IN, INFO)
INTEGER*8 N, INFO
INTEGER*8 IN(*)
DOUBLE PRECISION LAMBDA, TOL
DOUBLE PRECISION A(*), B(*), C(*), D(*)
F95 INTERFACE
SUBROUTINE LAGTF([N], A, LAMBDA, B, C, TOL, D, IN, [INFO])
INTEGER :: N, INFO
INTEGER, DIMENSION(:) :: IN
REAL(8) :: LAMBDA, TOL
REAL(8), DIMENSION(:) :: A, B, C, D
SUBROUTINE LAGTF_64([N], A, LAMBDA, B, C, TOL, D, IN, [INFO])
INTEGER(8) :: N, INFO
INTEGER(8), DIMENSION(:) :: IN
REAL(8) :: LAMBDA, TOL
REAL(8), DIMENSION(:) :: A, B, C, D
C INTERFACE
#include <sunperf.h>
void dlagtf(int n, double *a, double lambda, double *b, double *c, dou‐
ble tol, double *d, int *in, int *info);
void dlagtf_64(long n, double *a, double lambda, double *b, double *c,
double tol, double *d, long *in, long *info);
PURPOSEdlagtf factorizes the matrix (T - lambda*I), where T is an n by n
tridiagonal matrix and lambda is a scalar, as where P is a permutation
matrix, L is a unit lower tridiagonal matrix with at most one non-zero
sub-diagonal elements per column and U is an upper triangular matrix
with at most two non-zero super-diagonal elements per column.
The factorization is obtained by Gaussian elimination with partial piv‐
oting and implicit row scaling.
The parameter LAMBDA is included in the routine so that DLAGTF may be
used, in conjunction with DLAGTS, to obtain eigenvectors of T by
inverse iteration.
ARGUMENTS
N (input) The order of the matrix T.
A (input/output)
On entry, A must contain the diagonal elements of T.
On exit, A is overwritten by the n diagonal elements of the
upper triangular matrix U of the factorization of T.
LAMBDA (input)
On entry, the scalar lambda.
B (input/output)
On entry, B must contain the (n-1) super-diagonal elements of
T.
On exit, B is overwritten by the (n-1) super-diagonal ele‐
ments of the matrix U of the factorization of T.
C (input/output)
On entry, C must contain the (n-1) sub-diagonal elements of
T.
On exit, C is overwritten by the (n-1) sub-diagonal elements
of the matrix L of the factorization of T.
TOL (input/output)
On entry, a relative tolerance used to indicate whether or
not the matrix (T - lambda*I) is nearly singular. TOL should
normally be chose as approximately the largest relative error
in the elements of T. For example, if the elements of T are
correct to about 4 significant figures, then TOL should be
set to about 5*10**(-4). If TOL is supplied as less than eps,
where eps is the relative machine precision, then the value
eps is used in place of TOL.
D (output)
On exit, D is overwritten by the (n-2) second super-diagonal
elements of the matrix U of the factorization of T.
IN (output)
On exit, IN contains details of the permutation matrix P. If
an interchange occurred at the kth step of the elimination,
then IN(k) = 1, otherwise IN(k) = 0. The element IN(n)
returns the smallest positive integer j such that
abs( u(j,j) ).le. norm( (T - lambda*I)(j) )*TOL,
where norm( A(j) ) denotes the sum of the absolute values of
the jth row of the matrix A. If no such j exists then IN(n)
is returned as zero. If IN(n) is returned as positive, then a
diagonal element of U is small, indicating that (T -
lambda*I) is singular or nearly singular,
INFO (output)
= 0 : successful exit
6 Mar 2009 dlagtf(3P)
